How Can We Maximize Phylogenetic Diversity? Parameterized Approaches for Networks

Authors Mark Jones , Jannik Schestag

Thumbnail PDF


  • Filesize: 0.74 MB
  • 12 pages

Document Identifiers

Author Details

Mark Jones
  • TU Delft, The Netherlands
Jannik Schestag
  • TU Delft, The Netherlands
  • Friedrich-Schiller-Universität Jena, Germany

Cite AsGet BibTex

Mark Jones and Jannik Schestag. How Can We Maximize Phylogenetic Diversity? Parameterized Approaches for Networks. In 18th International Symposium on Parameterized and Exact Computation (IPEC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 285, pp. 30:1-30:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


Phylogenetic Diversity (PD) is a measure of the overall biodiversity of a set of present-day species (taxa) within a phylogenetic tree. We consider an extension of PD to phylogenetic networks. Given a phylogenetic network with weighted edges and a subset S of leaves, the all-paths phylogenetic diversity of S is the summed weight of all edges on a path from the root to some leaf in S. The problem of finding a bounded-size set S that maximizes this measure is polynomial-time solvable on trees, but NP-hard on networks. We study the latter from a parameterized perspective. While this problem is W[2]-hard with respect to the size of S (and W[1]-hard with respect to the size of the complement of S), we show that it is FPT with respect to several other parameters, including the phylogenetic diversity of S, the acceptable loss of phylogenetic diversity, the number of reticulations in the network, and the treewidth of the underlying graph.

Subject Classification

ACM Subject Classification
  • Theory of computation → Fixed parameter tractability
  • Theory of computation → W hierarchy
  • Applied computing → Bioinformatics
  • Phylogenetic Networks
  • Phylogenetic Diversity
  • Parameterized Complexity
  • W-hierarchy
  • FPT algorithms


  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    PDF Downloads


  1. Markus Bläser. Computing small Partial Coverings. Information Processing Letters, 85(6):327-331, 2003. Google Scholar
  2. Magnus Bordewich, Charles Semple, and Kristina Wicke. On the Complexity of optimising variants of Phylogenetic Diversity on Phylogenetic Networks. Theoretical Computer Science, 917:66-80, 2022. Google Scholar
  3. Olga Chernomor, Steffen Klaere, Arndt von Haeseler, and Bui Quang Minh. Split Diversity: Measuring and Optimizing Biodiversity using Phylogenetic Split Networks, pages 173-195. Springer International Publishing, 2016. Google Scholar
  4. Marek Cygan, Holger Dell, Daniel Lokshtanov, Dániel Marx, Jesper Nederlof, Yoshio Okamoto, and et al. On Problems as hard as CNF-SAT. ACM Transactions on Algorithms (TALG), 12(3):1-24, 2016. Google Scholar
  5. Marek Cygan, Fedor V. Fomin, Lukasz Kowalik, Daniel Lokshtanov, Dániel Marx, Marcin Pilipczuk, Michal Pilipczuk, and Saket Saurabh. Parameterized Algorithms. Springer, 2015. Google Scholar
  6. Rodney G. Downey and Michael R. Fellows. Fixed-Parameter tractability and completeness II: On completeness for W[1]. Theoretical Computer Science, 141(1-2):109-131, 1995. Google Scholar
  7. Rodney G. Downey and Michael R. Fellows. Fundamentals of Parameterized Complexity. Texts in Computer Science. Springer, 2013. Google Scholar
  8. Daniel P. Faith. Conservation evaluation and Phylogenetic Diversity. Biological Conservation, 61(1):1-10, 1992. Google Scholar
  9. Michael Fuchs and Emma Yu Jin. Equality of Shapley value and fair proportion index in phylogenetic trees. Journal of mathematical biology, 71:1133-1147, 2015. Google Scholar
  10. Frank Gurski, Carolin Rehs, and Jochen Rethmann. Knapsack Problems: A parameterized point of view. Theoretical Computer Science, 775:93-108, 2019. Google Scholar
  11. Claus-Jochen Haake, Akemi Kashiwada, and Francis Edward Su. The Shapley value of Phylogenetic Trees. Journal of mathematical biology, 56(4):479-497, 2008. Google Scholar
  12. Klaas Hartmann. The equivalence of two Phylogenetic Diodiversity measures: the Shapley value and Fair Proportion index. Journal of Mathematical Biology, 67:1163-1170, 2013. Google Scholar
  13. Daniel H. Huson, Regula Rupp, and Celine Scornavacca. Phylogenetic Networks: Concepts, Algorithms and Applications. Cambridge University Press, 2010. Google Scholar
  14. Nick J.B. Isaac, Samuel T. Turvey, Ben Collen, Carly Waterman, and Jonathan E.M. Baillie. Mammals on the EDGE: Conservation Priorities Based on Threat and Phylogeny. PLOS ONE, 2(3):1-7, 2007. Google Scholar
  15. Bingkai Lin. A simple gap-producing Reduction for the parameterized Set Cover Problem. arXiv preprint arXiv:1902.03702, 2019. Google Scholar
  16. Fabio Pardi and Nick Goldman. Species Choice for Comparative Genomics: Being Greedy Works. PLoS Genetics, 1, 2005. Google Scholar
  17. David W. Redding and Arne Ø. Mooers. Incorporating evolutionary measures into conservation prioritization. Conservation Biology, 20(6):1670-1678, 2006. Google Scholar
  18. Andreas Spillner, Binh T. Nguyen, and Vincent Moulton. Computing Phylogenetic Diversity for Split Systems. IEEE/ACM Transactions on Computational Biology and Bioinformatics, 5(2):235-244, 2008. Google Scholar
  19. Mike Steel. Phylogenetic Diversity and the greedy algorithm. Systematic Biology, 54(4):527-529, 2005. Google Scholar
  20. H. Martin Weingartner. Capital budgeting of interrelated projects: survey and synthesis. Management Science, 12(7):485-516, 1966. Google Scholar
  21. Kristina Wicke and Mareike Fischer. Phylogenetic Diversity and biodiversity indices on Phylogenetic Networks. Mathematical Biosciences, 298:80-90, 2018. Google Scholar